Representations of Growth and Decay
This lesson is optional. Its goal is for students to review different representations (descriptions, tables, graphs, equations) of exponential functions encountered in a previous course before they dive into more rigorous work with exponential functions in this unit. Students also evaluate functions at integer input values, including making sense of negative inputs in context. Later in the unit, students will begin looking at evaluating exponential functions at fractional input values, such as an input of \(\frac12\) to mean 5 years when an input of 1 means 1 decade.
Throughout this lesson, students repeatedly identify how different exponential functions change by equal factors over equal intervals and use this structure to produce tables, graphs, and equations that represent exponential change (MP7).
- Explain (in writing) the meaning of different constants in an expression representing an exponential function.
- Interpret equations and graphs that represent exponential functions in context.
- Let’s revisit ways to represent exponential change.
- I understand that exponential functions change by equal factors over equal intervals.
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